\contentsline {chapter}{\numberline {1}Introduction and basic equations}{5}{chapter.1}
\contentsline {section}{\numberline {1.1}Introduction}{5}{section.1.1}
\contentsline {subsection}{\numberline {1.1.1}Notation}{5}{subsection.1.1.1}
\contentsline {section}{\numberline {1.2}Linear elasticity}{5}{section.1.2}
\contentsline {subsection}{\numberline {1.2.1}Linear kinematics}{5}{subsection.1.2.1}
\contentsline {subsection}{\numberline {1.2.2}Equlibrium equations}{6}{subsection.1.2.2}
\contentsline {subsection}{\numberline {1.2.3}Constitutive equations}{7}{subsection.1.2.3}
\contentsline {subsection}{\numberline {1.2.4}Voight notation}{8}{subsection.1.2.4}
\contentsline {subsection}{\numberline {1.2.5}Boundary value problem in small strain elasticity}{8}{subsection.1.2.5}
\contentsline {subsubsection}{Strong form}{8}{section*.3}
\contentsline {subsubsection}{Weak form}{9}{section*.4}
\contentsline {subsection}{\numberline {1.2.6}Finite element discretization}{9}{subsection.1.2.6}
\contentsline {chapter}{\numberline {2}Solution procedures}{11}{chapter.2}
\contentsline {section}{\numberline {2.1}Solution procedures for nonlinear systems}{11}{section.2.1}
\contentsline {subsection}{\numberline {2.1.1}Newton-Raphson method}{11}{subsection.2.1.1}
\contentsline {subsection}{\numberline {2.1.2}Arc-length method}{12}{subsection.2.1.2}
\contentsline {section}{\numberline {2.2}Non-stationary linear transport model}{14}{section.2.2}
\contentsline {section}{\numberline {2.3}Non-stationary nonlinear transport model}{15}{section.2.3}
\contentsline {subsection}{\numberline {2.3.1}Heat flux from radiation}{16}{subsection.2.3.1}
\contentsline {section}{\numberline {2.4}Transient incompressible flow - Lagrangian Particle Method}{16}{section.2.4}
\contentsline {subsection}{\numberline {2.4.1}Lagrangian governing equations of incompressible fluid}{16}{subsection.2.4.1}
\contentsline {subsection}{\numberline {2.4.2}Time discretization}{17}{subsection.2.4.2}
\contentsline {subsection}{\numberline {2.4.3}Fractional step scheme}{17}{subsection.2.4.3}
\contentsline {subsection}{\numberline {2.4.4}Spatial discretization}{19}{subsection.2.4.4}
\contentsline {chapter}{\numberline {3}Elements}{21}{chapter.3}
\contentsline {chapter}{\numberline {4}Constitutive Equations}{23}{chapter.4}
\contentsline {section}{\numberline {4.1}Isotropic damage model}{23}{section.4.1}
\contentsline {section}{\numberline {4.2}Multisurface plasticity driver - MPlasticMaterial class}{24}{section.4.2}
\contentsline {subsection}{\numberline {4.2.1}Plasticity overview}{24}{subsection.4.2.1}
\contentsline {subsection}{\numberline {4.2.2}Closest-point return algorithm}{25}{subsection.4.2.2}
\contentsline {subsection}{\numberline {4.2.3}Algorithmic stiffness}{28}{subsection.4.2.3}
\contentsline {subsection}{\numberline {4.2.4}Implementation of particular models}{28}{subsection.4.2.4}
\contentsline {chapter}{\numberline {5}Boundary conditions}{29}{chapter.5}
\contentsline {chapter}{Bibliography}{29}{section*.5}
